Pseudoscalar production in electromagnetic fields by a Schwinger-like mechanism

In this talk I report on some recent calculations on the production of pseudoscalars from intense electromagnetic fields. Talk at QED2000, Trieste (October 2000) 1 Decay of classical background fields into pseudoscalars We would like to calculate the effective action for the background electromagnetic E and B fields, eeff [E,B] = ∫ Dφ e (1) when integrating a pseudoscalar φ of mass m, that has an action S with a coupling to the E and B fields of the form S[φ,E,B] = ∫ dx 1 2 φ(x) [ −∂ −m + f(x,E,B) ] φ(x) (2) Using the identities i ∂Seff [E,B] ∂m2 = − ∫ Dφ φ e ∫ Dφ eiS[φ,E,B] = − 2 ∫ dx G (x, x;E,B) = − 2 ∫ dx ∫ dp (2π)4 G (p;E,B) (3) we can express the effective Lagrangian of the background fields in terms of the Green’s function G(p) of φ propagating in these fields. Leff [E,B] = i 2 ∫ dm ∫ dp (2π)4 G (p;E,B) (4) Our objective now is to determine 1) G(p) and 2) Leff . 1) The action (1) contains the interaction Lagrangian LI(x) = 1 2 f(x)φ(x) (5) and leads to the following equation for the Green function [ ∂ +m − f(x) ] G(x, 0) = δ(x) (6) We will approximate f(x) by its Taylor series near the reference point x = 0 up to second order, f(x) = α+ βμx μ + γ μνx x (7)